Set in the then-future year of 1983, the series tells the tale of the crew and passengers of a sub-orbital transport spaceship called the Spindrift. In the pilot episode, the Spindrift is en route from Los Angeles to London via the ultra-fast route of a parabolic trajectory. Just beyond Earth's boundary with space, the Spindrift encounters a strange space storm and is transported to a mysterious planet where everything is twelve times larger than its counterpart on Earth. The Spindrift crew calls the inhabitants "the giants". Given relative proportions shown on the show, the giants are about 72 feet tall (similar to Gulliver's situation in the second part of "Gulliver's Travels", when he is in the land of Brobdingnag). Everything on their planet is built to their scale — buildings, cars, animals, etc. The Spindrift crashes on this planet and becomes inoperable.

These giants are humanoid in form, and though their society resembles in some respects that of 1960's America, their government is totalitarian. However few precise details are given and no governmental symbols are ever seen. The giant government has offered a reward for the capture of the tiny Earth people, presumably because of the Earth's superior technology. Episodes often have the plot of giants capturing one of the passengers or crew with the rest having to rescue him or her. The Earth people avoid capture most of the time because their spaceship is hidden in a forest outside the city. They also occasionally form alliances with individual giants to achieve some commonly beneficial purpose. And they're always running.